Crystalline materials, from salt to diamond, are ubiquitous in nature. Until recently the very word 'crystal' was thought to be synonymous with a regular and symmetric periodic structure. But 20 years ago an unexpected discovery shook the foundations of crystallography to the core. A new class of materials, now named quasicrystals, defied the rules by showing a new, more complicated type of order that could provide new materials for nanotechnology and super-slippery surfaces.

In conventional crystals a single building block, the unit cell, is repeated over and over again to give atomic order over the short and long range. Quasicrystals are alloy materials which use several building blocks to form a crystal that has a complex tessellated structure that never exactly repeats. For ordinary crystals the rules of crystallography say that the repeating atomic structure must obey 1-, 2-, 3-, 4- or 6-fold symmetry. This means that the appearance of the structure does not change when rotated through a whole circle, half circle etc. Because of the absence of periodicity, quasicrystals may exhibit 5-, 10-fold or other symmetries previously thought to be forbidden in crystalline materials.

'Understanding the mathematics of these structures has drawn on centuries of contributions from famous mathematicians and scientists like Fibonacci, Kepler and Penrose', says Uwe Grimm, a mathematician studying quasicrystal structure at the Open University. 'Since their discovery, great progress has been made in synthesising theoretical descriptions of quasicrystals. However, gaps in our knowledge remain with respect to understanding the formation of their intricate atomic order and predicting physical characteristics from a given structure.'

Many of the known quasicrystals are alloys of three elements that individually are good metals, so it is surprising that the crystals exhibit unexpected properties, such as relatively low electrical conductivity that increases strongly with temperature. This is opposite to the behaviour found in metals and is often termed 'anti-metallic'.